How many 5-letter words that have the letter 'x' are possible? Letters may be repeated, and the words don't have to be meaningful. (Hint: First count the words without 'x' .) Your answer is:

2115751

Step-by-step explanation:

Solution:

- The number of 5 letter words that contain x is the number of 5 letter words overall minus the number of 5 letter of words without x.

                  How many 5 letter words are there overall?

- The first letter could be one of 26 letters. The same could be said about the second letter, and the third, and the fourth and the fifth .. so on.

- So the number of 5 letter words overall is:

                        26x26x26x26x26 = 26^5 = 11881376

          How many 5 letter words are there that do not contain x?

- The first letter could be one of 25 letters (it could be one of any of the other 25 letters but not x). The second letter could also be one of 25 letters, and so could the third, and so could the fourth, and so could the fifth.

- So the number of 5 letter words that do not contain x is:

                        25x25x25x25x25 = 25^5 = 9765625

- So the number of 5 letter words that contain x is:

                      26^5 - 25^5 = 11881376 - 9765625 = 2115751.